Simultaneous Image Restoration and Hyperparameter Estimation for Incomplete Data by a Cumulant Analysis

The purpose of this report is first to show the main properties of Gibbs distributions considered as exponential statistics on finite spaces, as well as their sampling and annealing properties. Moreover, the definition and use of their cumulant expansions enables to exhibit other important properties of such distributions. Last, we tackle the problem of hyperparameter estimation in an incomplete data frame for image restoration purposes. A detailed analysis of several joint restoration-estimation methods using generalized stochastic gradient algorithms is presented, requiring infinite, continuous configuration spaces. Using once again cumulant analysis and its relationship with Statistical Physics allows us to propose new algorithms and to extend them to an explicit boundary frame

Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations

We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given initial location to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. We formulate the problem using the framework of Lagrangian mechanics. We derive closed-form formulas for the optimal trajectory when the traffic intensity is quadratic (single-phase) using Hamilton-Jacobi equations. When the traffic intensity is bi-phase, i.e. made of two quadratics, we provide necessary conditions of optimality that allow us to propose a gradient-based algorithm and a new algorithm based on the linear control properties of the quadratic model. These two solutions are of very low complexity because they rely on fast convergence numerical schemes and closed form formulas. These two approaches return a trajectory satisfying the necessary conditions of optimality. At last, we propose a data processing procedure based on a modified K-means algorithm to derive a bi-phase model and an optimal trajectory simulation from real traffic data.Comment: 30 pages, 10 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1812.0875

Réseaux Bayésiens Dynamiques pour la reconnaissance des caractères imprimés dégradés

Le but de ce travail est de présenter une nouvelle approche pour la reconnaissance des caractères imprimés dégradés. Notre approche consiste à construire deux chaînes de Markov cachées [HMMs] à l'aide des réseaux bayésiens dynamiques, nommées HMM vertical et horizontal. Un HMM-vertical (respectivement HMM-horizontal) est un modèle qui prend pour séquence d'entrée les colonnes de pixels du caractère (respectivement les lignes de pixels). Nous couplons ensuite ces chaînes suivant deux modèles de couplage en utilisant les réseaux bayésiens dynamiques. Les résultats expérimentaux montrent que les modèles de couplage augmentent le taux de reconnaissance de 8 % à 10 % relativement au système de reconnaissance utilisant les modèles non couplés

Joint filtering of SAR amplitude and interferometric phase with graph-cuts

Like other coherent imaging modalities, synthetic aperture radar (SAR) images suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. values respectively less (sub-figure 1, under-regularized), equal (sub-figure 2) or greater (sub figure 3, over-regularized) than βopt. Section IV-B presents some results of the joint regularization of high-resolution interferometric SAR images on two datasets: a 1200 × 1200 pixels region of interest from Toulouse city, France (figure 5), and a 1024 × 682 pixels region of interest from Saint-Paul sur Mer, France (figure 7). From the regularized images shown, it can be noticed that the noise has been efficiently reduced both in amplitude and phase images. The sharp transitions in the phase image that correspond to man-made structures are well preserved. Joint regularization gives more precise contours than independent regularization as they are co-located from the phase and amplitude images. Small objects also tend to be better preserved by joint-regularization as illustrated in figure 6 which shows an excerpt of a portion of streets with several aligned streetlights visible as brighter dots (higher reflectivity as well as higher altitude). values respectively less (sub-figure 1, under-regularized), equal (sub-figure 2) or greater (sub figure 3, over-regularized) than βopt. Section IV-B presents some results of the joint regularization of high-resolution interferometric SAR images on two datasets: a 1200 × 1200 pixels region of interest from Toulouse city, France (figure 5), and a 1024 × 682 pixels region of interest from Saint-Paul sur Mer, France (figure 7). From the regularized images shown, it can be noticed that the noise has been efficiently reduced both in amplitude and phase images. The sharp transitions in the phase image that correspond to man-made structures are well preserved. Joint regularization gives more precise contours than independent regularization as they are co-located from the phase and amplitude images. Small objects also tend to be better preserved by joint-regularization as illustrated in figure 6 which shows an excerpt of a portion of streets with several aligned streetlights visible as brighter dots (higher reflectivity as well as higher altitude).L’imagerie radar à ouverture synthétique (SAR), comme d’autres modalités d’imagerie cohérente, souffre de la présence du chatoiement (speckle). Cette perturbation rend difficile l’interprétation automatique des images et le filtrage est souvent une étape nécessaire à l’utilisation d’algorithmes de traitement d’images classiques. De nombreuses approches ont été proposées pour filtrer les images corrompues par un bruit de chatoiement. La modélisation par champs de Markov (CdM) fournit un cadre adapté pour exprimer à la fois les contraintes sur l’attache aux données et les propriétés désirées sur l’image filtrée. Dans ce contexte la minimisation de la variation totale a été abondamment utilisée afin de limiter les oscillations dans l’image régularisée tout en préservant les bords. Le bruit de chatoiement suit une distribution de probabilité à queue lourde et la formulation par CdM conduit à un problème de minimisation mettant en jeu des attaches aux données non-convexes. Une telle minimisation peut être obtenue par une approche d’optimisation combinatoire en calculant des coupures minimales de graphes. Bien que cette optimisation puisse être menée en théorie, ce type d’approche ne peut être appliqué en pratique sur les images de grande taille rencontrées dans les applications de télédétection à cause de leur grande consommation de mémoire. Le temps de calcul des algorithmes de minimisation approchée (en particulier α-extension) est généralement trop élevé quand la régularisation jointe de plusieurs images est considérée. Nous montrons qu’une solution satisfaisante peut être obtenue, en quelques itérations, en menant une exploration de l’espace de recherche avec de grands pas. Cette dernière est réalisée en utilisant des techniques de coupures minimales. Cet algorithme est appliqué pour régulariser de manière jointe à la fois l’amplitude et la phase interférométrique d’images SAR en milieu urbain

Simultaneous Image Restoration and Hyperparameter Estimation for Incomplete Data by a Cumulant Analysis

: The purpose of this report is first to show the main properties of Gibbs distributions considered as exponential statistics on finite spaces, as well as their sampling and annealing properties. Moreover, the definition and use of their cumulant expansions enables to exhibit other important properties of such distributions. Last, we tackle the problem of hyperparameter estimation in an incomplete data frame for image restoration purposes. A detailed analysis of several joint restoration-estimation methods using generalized stochastic gradient algorithms is presented, requiring infinite, continuous configuration spaces. Using once again cumulant analysis and its relationship with Statistical Physics allows us to propose new algorithms and to extend them to an explicit boundary frame. Key-words: exponential statistics, Gibbs distributions, hyperparameters, restoration, estimation, stochastic gradient. (Rsum : tsvp) * E-mail: [email protected]. This work was done while the author was..

Restauration et segmentation d'images de télédétection (une étude de méthodes accélérées)

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Relaxation d'images de classification et modèles de la physique statistique

International audienceWe show in this paper the deep relationship between classic models from Statistical Physics and Markovian Random Fields models used in image labelling. We present as an application a markovian relaxation method for enhancement and relaxation of previously classified images . An energy function is defined, which depends only on the labels and on their initial value . The main a priori pixel knowledge results from the confusion matrix of the reference samples used for initial classification . The energy to be minimized includes also terms ensuring simultaneous spatial label regularty, growth of some classes and disparition of some others. The method allows for example to reclassify previous rejection class pixels in their spatial environment . Last we present some results on Remote Sensing multispectral and geological ore images, comparing the performances of Iterated Conditional Modes (ICM) and Simulated Annealing (SA) . Very low CPU time was obtained due to the principle of the method, working on labels instead of gray levels .Nous montrons dans cet article la relation profonde entre certains modèles d'énergie provenant de la Physique Statistique utilisés et les modèles utilisés en champ de Markov pour l'étiquetage d'images. Nous présentons comme application une méthode markovienne de relaxation et d'amélioration d'images préclassifiées. On définit pour cela une fonction énergie ne dépendant que des labels et de leur valeur initiale, la connaissance a priori sur l'image provenant de la matrice de confusion déduite des échantillons de référence utilisés pour la classification initiale. La fonction à minimiser inclut divers termes assurant la régularité spatiale des labels, la croissance ou la disparition de certaines classe